How can i disconnect part of mesh, reconnect it to another part and make it a part of different UV island?
This is old question but I'd figure I'll post possible answer anyways because someone else might google this. 

I'd just pin (select these verts and press p) the vertices in uv editor that need to stay put. Leave all seams unpinned. Then just press u and do basic uvunwrap the whole mesh. Only those vertices that you wanted to move should move. If you get weird result then you probably have a missing seam, wrong vertice pinned, hidden geometry in edit mode or something else. After the uvunwrap press alt-p in uv editor to get rid of the pin tool.